Assumptions for using (1-)100% Confidence Interval for two populations when σ is known

1) Two samples are random & independent

2) Both samples came from two independent, normal populations

3) σ12 (σ1) and σ22(σ2) are known

Assumptions for using (1-)100% Confidence Interval for t-distribution

1) Two samples are random & independent

2) Both samples came from normal populations

3) σ12 (σ1) and σ22(σ2) are unknown but equal

The point estimator for the unknown common variance σ2is

sp2

To test the hypothesis about unknown p1 & p2

we combine the information given in both samples to compute estimated variance of p1 & p2

To construct a (1-)100% confidence interval for p1 and p2

we do NOT combine the information contained in both samples to compute the estimated variance

A goodness of fit test

Tests the Null Hypothesis that the observed frequencies follow a pattern or theoretical distribution. The test is goodness-of-fit because the hypothesis tested is how good the observed frequencies fit a given pattern

The -squared goodness of fit test

used to test whether of not the sampled multinomial data is in agreement with the hypothesized distribution. OR Testing 3 or more unknown population proportions.

In a goodness of fit test, when is the Null Hypothesis rejected?

A good agreement between the observed and expected frequencies results in a small value of . A perfect agreement would result in =0. Thus the Null Hypothesis is rejected if is large [upper tail test]

For tests of Independence between Criterion A and B...
Ho: The two criteria A&B are

INDEPENDENT or not related (HoI)

For tests of Independence between Criterion A and B...
HA: The two criteria A&B are

DEPENDENT or related (HAD)

For tests of independence, is

For tests of Independence, Eij=

For a 2x2 Contingency table, testing for independence for two criteria is equivalent to testing

H0: P1=P2 vs HA:P1≠P2

Test of Homogeneity

A test of homogeneity involves testing the

H0: the proportions of elements with certain characteristics in two or more different populations are the same